Abstract

Part II uses the foundations of Part I [35] to define constraint equations for
2D-3D pose estimation of different corresponding entities. Most articles on
pose estimation concentrate on specific types of correspondences, mostly
between points, and only rarely use line correspondences. The first aim of this
part is to extend pose estimation scenarios to correspondences of an extended
set of geometric entities. In this context we are interested to relate the
following (2D) image and (3D) model types: 2D point/3D point, 2D line/3D point,
2D line/3D line, 2D conic/3D circle, 2D conic/3D sphere. Furthermore, to handle
articulated objects, we describe kinematic chains in this context in a similar
manner. We ensure that all constraint equations end up in a distance measure in
the Euclidean space, which is well posed in the context of noisy data. We also
discuss the numerical estimation of the pose. We propose to use linearized
twist transformations which result in well conditioned and fast solvable
systems of equations. The key idea is not to search for the representation of
the Lie group, describing the rigid body motion, but for the representation of
their generating Lie algebra. This leads to real-time capable algorithms.